Study with the several resources on Docsity
Earn points by helping other students or get them with a premium plan
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
The fall, 2009 exam 3a for the m340l linear algebra course. It includes instructions, 8 problems, and scoring rubrics for students. The problems cover topics such as eigenvalues, eigenvectors, diagonalizability, linear transformations, and orthogonal bases.
Typology: Exams
1 / 6
This page cannot be seen from the preview
Don't miss anything!
Your name:
Your UTEID:
Show all your work on these pages. Be organized and neat. Your work should be your own; there should be no talking, reading notes, checking laptops, using cellphones,....
? If so, find a basis
for its eigenspace. If not, justify your answer.
= 5b 1 −^2 b 2 and^ T
= 2b 1 +^ b 2 and^ T
= b 1 + 4b 2.
(a) (6 points) Calculate and simplify T
.
(b) (6 points) What is the matrix for T relative to the standard basis for R^3 and the basis B for V?
(c) (6 points) Suppose C is another basis for V , where
c 1 = 5b 1 + 2b 2 ,
c 2 = 7b 1 + 3b 2. What is the matrix for T relative to the standard basis for R^3 and the basis C for V?
u 1 =
, u 2 =
, u 3 =
.
(a) (4 points) Verify that {u 1 , u 2 , u 3 } is an orthogonal basis for W.
(b) (10 pts.) Write y =
as the sum of a vector in W and a vector in W ⊥.
(c) (4 points) Find the distance from y to the subspace W.
(d) (6 points) Find a basis for W ⊥.
